Inducing schemes for multi-dimensional piecewise expanding maps

Abstract

<p style='text-indent:20px;'>We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical properties of dynamical systems with some hyperbolicity. As an application we check the conditions for the first return map of a class of multi-dimensional non-Markov, non-conformal intermittent maps.</p>

Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps

“…The reinducing step, Lemma 3.1 below, makes use of recent work [23] based on the method of standard pairs [12,22], and gives precise joint control on the first return time to Y and the reinducing return time (denoted respectively as ϕ and ρ below). As already noted, the reinducing approach adopted in [10] seems not applicable for the examples in this paper and in any case gives much less control on return times.…”

“…This section is devoted to the proof of Lemma 3.1. The main step is to verify the hypotheses of Theorem 3 of [23]. This is done using Theorem A.1 below.…”